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/*
 * Copyright (C) 2012 The Guava Authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
 * in compliance with the License. You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software distributed under the License
 * is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
 * or implied. See the License for the specific language governing permissions and limitations under
 * the License.
 */

package com.google.common.util.concurrent;

import static java.lang.Math.min;
import static java.util.concurrent.TimeUnit.SECONDS;

import com.google.common.annotations.GwtIncompatible;
import com.google.common.math.LongMath;
import java.util.concurrent.TimeUnit;

@GwtIncompatible
abstract class SmoothRateLimiter extends RateLimiter {
  /*
   * How is the RateLimiter designed, and why?
   *
   * The primary feature of a RateLimiter is its "stable rate", the maximum rate that is should
   * allow at normal conditions. This is enforced by "throttling" incoming requests as needed, i.e.
   * compute, for an incoming request, the appropriate throttle time, and make the calling thread
   * wait as much.
   *
   * The simplest way to maintain a rate of QPS is to keep the timestamp of the last granted
   * request, and ensure that (1/QPS) seconds have elapsed since then. For example, for a rate of
   * QPS=5 (5 tokens per second), if we ensure that a request isn't granted earlier than 200ms after
   * the last one, then we achieve the intended rate. If a request comes and the last request was
   * granted only 100ms ago, then we wait for another 100ms. At this rate, serving 15 fresh permits
   * (i.e. for an acquire(15) request) naturally takes 3 seconds.
   *
   * It is important to realize that such a RateLimiter has a very superficial memory of the past:
   * it only remembers the last request. What if the RateLimiter was unused for a long period of
   * time, then a request arrived and was immediately granted? This RateLimiter would immediately
   * forget about that past underutilization. This may result in either underutilization or
   * overflow, depending on the real world consequences of not using the expected rate.
   *
   * Past underutilization could mean that excess resources are available. Then, the RateLimiter
   * should speed up for a while, to take advantage of these resources. This is important when the
   * rate is applied to networking (limiting bandwidth), where past underutilization typically
   * translates to "almost empty buffers", which can be filled immediately.
   *
   * On the other hand, past underutilization could mean that "the server responsible for handling
   * the request has become less ready for future requests", i.e. its caches become stale, and
   * requests become more likely to trigger expensive operations (a more extreme case of this
   * example is when a server has just booted, and it is mostly busy with getting itself up to
   * speed).
   *
   * To deal with such scenarios, we add an extra dimension, that of "past underutilization",
   * modeled by "storedPermits" variable. This variable is zero when there is no underutilization,
   * and it can grow up to maxStoredPermits, for sufficiently large underutilization. So, the
   * requested permits, by an invocation acquire(permits), are served from:
   *
   * - stored permits (if available)
   *
   * - fresh permits (for any remaining permits)
   *
   * How this works is best explained with an example:
   *
   * For a RateLimiter that produces 1 token per second, every second that goes by with the
   * RateLimiter being unused, we increase storedPermits by 1. Say we leave the RateLimiter unused
   * for 10 seconds (i.e., we expected a request at time X, but we are at time X + 10 seconds before
   * a request actually arrives; this is also related to the point made in the last paragraph), thus
   * storedPermits becomes 10.0 (assuming maxStoredPermits >= 10.0). At that point, a request of
   * acquire(3) arrives. We serve this request out of storedPermits, and reduce that to 7.0 (how
   * this is translated to throttling time is discussed later). Immediately after, assume that an
   * acquire(10) request arriving. We serve the request partly from storedPermits, using all the
   * remaining 7.0 permits, and the remaining 3.0, we serve them by fresh permits produced by the
   * rate limiter.
   *
   * We already know how much time it takes to serve 3 fresh permits: if the rate is
   * "1 token per second", then this will take 3 seconds. But what does it mean to serve 7 stored
   * permits? As explained above, there is no unique answer. If we are primarily interested to deal
   * with underutilization, then we want stored permits to be given out /faster/ than fresh ones,
   * because underutilization = free resources for the taking. If we are primarily interested to
   * deal with overflow, then stored permits could be given out /slower/ than fresh ones. Thus, we
   * require a (different in each case) function that translates storedPermits to throttling time.
   *
   * This role is played by storedPermitsToWaitTime(double storedPermits, double permitsToTake). The
   * underlying model is a continuous function mapping storedPermits (from 0.0 to maxStoredPermits)
   * onto the 1/rate (i.e. intervals) that is effective at the given storedPermits. "storedPermits"
   * essentially measure unused time; we spend unused time buying/storing permits. Rate is
   * "permits / time", thus "1 / rate = time / permits". Thus, "1/rate" (time / permits) times
   * "permits" gives time, i.e., integrals on this function (which is what storedPermitsToWaitTime()
   * computes) correspond to minimum intervals between subsequent requests, for the specified number
   * of requested permits.
   *
   * Here is an example of storedPermitsToWaitTime: If storedPermits == 10.0, and we want 3 permits,
   * we take them from storedPermits, reducing them to 7.0, and compute the throttling for these as
   * a call to storedPermitsToWaitTime(storedPermits = 10.0, permitsToTake = 3.0), which will
   * evaluate the integral of the function from 7.0 to 10.0.
   *
   * Using integrals guarantees that the effect of a single acquire(3) is equivalent to {
   * acquire(1); acquire(1); acquire(1); }, or { acquire(2); acquire(1); }, etc, since the integral
   * of the function in [7.0, 10.0] is equivalent to the sum of the integrals of [7.0, 8.0], [8.0,
   * 9.0], [9.0, 10.0] (and so on), no matter what the function is. This guarantees that we handle
   * correctly requests of varying weight (permits), /no matter/ what the actual function is - so we
   * can tweak the latter freely. (The only requirement, obviously, is that we can compute its
   * integrals).
   *
   * Note well that if, for this function, we chose a horizontal line, at height of exactly (1/QPS),
   * then the effect of the function is non-existent: we serve storedPermits at exactly the same
   * cost as fresh ones (1/QPS is the cost for each). We use this trick later.
   *
   * If we pick a function that goes /below/ that horizontal line, it means that we reduce the area
   * of the function, thus time. Thus, the RateLimiter becomes /faster/ after a period of
   * underutilization. If, on the other hand, we pick a function that goes /above/ that horizontal
   * line, then it means that the area (time) is increased, thus storedPermits are more costly than
   * fresh permits, thus the RateLimiter becomes /slower/ after a period of underutilization.
   *
   * Last, but not least: consider a RateLimiter with rate of 1 permit per second, currently
   * completely unused, and an expensive acquire(100) request comes. It would be nonsensical to just
   * wait for 100 seconds, and /then/ start the actual task. Why wait without doing anything? A much
   * better approach is to /allow/ the request right away (as if it was an acquire(1) request
   * instead), and postpone /subsequent/ requests as needed. In this version, we allow starting the
   * task immediately, and postpone by 100 seconds future requests, thus we allow for work to get
   * done in the meantime instead of waiting idly.
   *
   * This has important consequences: it means that the RateLimiter doesn't remember the time of the
   * _last_ request, but it remembers the (expected) time of the _next_ request. This also enables
   * us to tell immediately (see tryAcquire(timeout)) whether a particular timeout is enough to get
   * us to the point of the next scheduling time, since we always maintain that. And what we mean by
   * "an unused RateLimiter" is also defined by that notion: when we observe that the
   * "expected arrival time of the next request" is actually in the past, then the difference (now -
   * past) is the amount of time that the RateLimiter was formally unused, and it is that amount of
   * time which we translate to storedPermits. (We increase storedPermits with the amount of permits
   * that would have been produced in that idle time). So, if rate == 1 permit per second, and
   * arrivals come exactly one second after the previous, then storedPermits is _never_ increased --
   * we would only increase it for arrivals _later_ than the expected one second.
   */

  
This implements the following function where coldInterval = coldFactor * stableInterval.

         ^ throttling
         |
   cold  +                  /
interval |                 /.
         |                / .
         |               /  .   ← "warmup period" is the area of the trapezoid between
         |              /   .     thresholdPermits and maxPermits
         |             /    .
         |            /     .
         |           /      .
  stable +----------/  WARM .
interval |          .   UP  .
         |          . PERIOD.
         |          .       .
       0 +----------+-------+--------------→ storedPermits
         0 thresholdPermits maxPermits


Before going into the details of this particular function, let's keep in mind the basics:

    
  
  1. The state of the RateLimiter (storedPermits) is a vertical line in this figure.
  
  2. When the RateLimiter is not used, this goes right (up to maxPermits)
  
  3. When the RateLimiter is used, this goes left (down to zero), since if we have
      storedPermits, we serve from those first
  
  4. When _unused_, we go right at a constant rate! The rate at which we move to the right is
      chosen as maxPermits / warmupPeriod. This ensures that the time it takes to go from 0 to
      maxPermits is equal to warmupPeriod.
  
  5. When _used_, the time it takes, as explained in the introductory class note, is equal to
      the integral of our function, between X permits and X-K permits, assuming we want to
      spend K saved permits.



In summary, the time it takes to move to the left (spend K permits), is equal to the area of
the function of width == K.

Assuming we have saturated demand, the time to go from maxPermits to thresholdPermits is
equal to warmupPeriod. And the time to go from thresholdPermits to 0 is warmupPeriod/2. (The
reason that this is warmupPeriod/2 is to maintain the behavior of the original implementation
where coldFactor was hard coded as 3.)

It remains to calculate thresholdsPermits and maxPermits.

    
  
  • The time to go from thresholdPermits to 0 is equal to the integral of the function
      between 0 and thresholdPermits. This is thresholdPermits * stableIntervals. By (5) it is
      also equal to warmupPeriod/2. Therefore
      
    
      thresholdPermits = 0.5 * warmupPeriod / stableInterval
      
    
  
  • The time to go from maxPermits to thresholdPermits is equal to the integral of the
      function between thresholdPermits and maxPermits. This is the area of the pictured
      trapezoid, and it is equal to 0.5 * (stableInterval + coldInterval) * (maxPermits -
      thresholdPermits). It is also equal to warmupPeriod, so
      
    
      maxPermits = thresholdPermits + 2 * warmupPeriod / (stableInterval + coldInterval)
      
    



/**
   * This implements the following function where coldInterval = coldFactor * stableInterval.
   *
   * <pre>
   *          ^ throttling
   *          |
   *    cold  +                  /
   * interval |                 /.
   *          |                / .
   *          |               /  .   ← "warmup period" is the area of the trapezoid between
   *          |              /   .     thresholdPermits and maxPermits
   *          |             /    .
   *          |            /     .
   *          |           /      .
   *   stable +----------/  WARM .
   * interval |          .   UP  .
   *          |          . PERIOD.
   *          |          .       .
   *        0 +----------+-------+--------------→ storedPermits
   *          0 thresholdPermits maxPermits
   * </pre>
   *
   * Before going into the details of this particular function, let's keep in mind the basics:
   *
   * <ol>
   *   <li>The state of the RateLimiter (storedPermits) is a vertical line in this figure.
   *   <li>When the RateLimiter is not used, this goes right (up to maxPermits)
   *   <li>When the RateLimiter is used, this goes left (down to zero), since if we have
   *       storedPermits, we serve from those first
   *   <li>When _unused_, we go right at a constant rate! The rate at which we move to the right is
   *       chosen as maxPermits / warmupPeriod. This ensures that the time it takes to go from 0 to
   *       maxPermits is equal to warmupPeriod.
   *   <li>When _used_, the time it takes, as explained in the introductory class note, is equal to
   *       the integral of our function, between X permits and X-K permits, assuming we want to
   *       spend K saved permits.
   * </ol>
   *
   * <p>In summary, the time it takes to move to the left (spend K permits), is equal to the area of
   * the function of width == K.
   *
   * <p>Assuming we have saturated demand, the time to go from maxPermits to thresholdPermits is
   * equal to warmupPeriod. And the time to go from thresholdPermits to 0 is warmupPeriod/2. (The
   * reason that this is warmupPeriod/2 is to maintain the behavior of the original implementation
   * where coldFactor was hard coded as 3.)
   *
   * <p>It remains to calculate thresholdsPermits and maxPermits.
   *
   * <ul>
   *   <li>The time to go from thresholdPermits to 0 is equal to the integral of the function
   *       between 0 and thresholdPermits. This is thresholdPermits * stableIntervals. By (5) it is
   *       also equal to warmupPeriod/2. Therefore
   *       <blockquote>
   *       thresholdPermits = 0.5 * warmupPeriod / stableInterval
   *       </blockquote>
   *   <li>The time to go from maxPermits to thresholdPermits is equal to the integral of the
   *       function between thresholdPermits and maxPermits. This is the area of the pictured
   *       trapezoid, and it is equal to 0.5 * (stableInterval + coldInterval) * (maxPermits -
   *       thresholdPermits). It is also equal to warmupPeriod, so
   *       <blockquote>
   *       maxPermits = thresholdPermits + 2 * warmupPeriod / (stableInterval + coldInterval)
   *       </blockquote>
   * </ul>
   */
  static final class SmoothWarmingUp extends SmoothRateLimiter {
    private final long warmupPeriodMicros;
    
The slope of the line from the stable interval (when permits == 0), to the cold interval
(when permits == maxPermits)

/**
     * The slope of the line from the stable interval (when permits == 0), to the cold interval
     * (when permits == maxPermits)
     */
    private double slope;

    private double thresholdPermits;
    private double coldFactor;

    SmoothWarmingUp(
        SleepingStopwatch stopwatch, long warmupPeriod, TimeUnit timeUnit, double coldFactor) {
      super(stopwatch);
      this.warmupPeriodMicros = timeUnit.toMicros(warmupPeriod);
      this.coldFactor = coldFactor;
    }

    @Override
    void doSetRate(double permitsPerSecond, double stableIntervalMicros) {
      double oldMaxPermits = maxPermits;
      double coldIntervalMicros = stableIntervalMicros * coldFactor;
      thresholdPermits = 0.5 * warmupPeriodMicros / stableIntervalMicros;
      maxPermits =
          thresholdPermits + 2.0 * warmupPeriodMicros / (stableIntervalMicros + coldIntervalMicros);
      slope = (coldIntervalMicros - stableIntervalMicros) / (maxPermits - thresholdPermits);
      if (oldMaxPermits == Double.POSITIVE_INFINITY) {
        // if we don't special-case this, we would get storedPermits == NaN, below
        storedPermits = 0.0;
      } else {
        storedPermits =
            (oldMaxPermits == 0.0)
                ? maxPermits // initial state is cold
                : storedPermits * maxPermits / oldMaxPermits;
      }
    }

    @Override
    long storedPermitsToWaitTime(double storedPermits, double permitsToTake) {
      double availablePermitsAboveThreshold = storedPermits - thresholdPermits;
      long micros = 0;
      // measuring the integral on the right part of the function (the climbing line)
      if (availablePermitsAboveThreshold > 0.0) {
        double permitsAboveThresholdToTake = min(availablePermitsAboveThreshold, permitsToTake);
        // TODO(cpovirk): Figure out a good name for this variable.
        double length =
            permitsToTime(availablePermitsAboveThreshold)
                + permitsToTime(availablePermitsAboveThreshold - permitsAboveThresholdToTake);
        micros = (long) (permitsAboveThresholdToTake * length / 2.0);
        permitsToTake -= permitsAboveThresholdToTake;
      }
      // measuring the integral on the left part of the function (the horizontal line)
      micros += (long) (stableIntervalMicros * permitsToTake);
      return micros;
    }

    private double permitsToTime(double permits) {
      return stableIntervalMicros + permits * slope;
    }

    @Override
    double coolDownIntervalMicros() {
      return warmupPeriodMicros / maxPermits;
    }
  }

  
This implements a "bursty" RateLimiter, where storedPermits are translated to zero throttling.
The maximum number of permits that can be saved (when the RateLimiter is unused) is defined in
terms of time, in this sense: if a RateLimiter is 2qps, and this time is specified as 10
seconds, we can save up to 2 * 10 = 20 permits.

/**
   * This implements a "bursty" RateLimiter, where storedPermits are translated to zero throttling.
   * The maximum number of permits that can be saved (when the RateLimiter is unused) is defined in
   * terms of time, in this sense: if a RateLimiter is 2qps, and this time is specified as 10
   * seconds, we can save up to 2 * 10 = 20 permits.
   */
  static final class SmoothBursty extends SmoothRateLimiter {
    
The work (permits) of how many seconds can be saved up if this RateLimiter is unused? 
/** The work (permits) of how many seconds can be saved up if this RateLimiter is unused? */
    final double maxBurstSeconds;

    SmoothBursty(SleepingStopwatch stopwatch, double maxBurstSeconds) {
      super(stopwatch);
      this.maxBurstSeconds = maxBurstSeconds;
    }

    @Override
    void doSetRate(double permitsPerSecond, double stableIntervalMicros) {
      double oldMaxPermits = this.maxPermits;
      maxPermits = maxBurstSeconds * permitsPerSecond;
      if (oldMaxPermits == Double.POSITIVE_INFINITY) {
        // if we don't special-case this, we would get storedPermits == NaN, below
        storedPermits = maxPermits;
      } else {
        storedPermits =
            (oldMaxPermits == 0.0)
                ? 0.0 // initial state
                : storedPermits * maxPermits / oldMaxPermits;
      }
    }

    @Override
    long storedPermitsToWaitTime(double storedPermits, double permitsToTake) {
      return 0L;
    }

    @Override
    double coolDownIntervalMicros() {
      return stableIntervalMicros;
    }
  }

  
The currently stored permits. 
/** The currently stored permits. */
  double storedPermits;

  
The maximum number of stored permits. 
/** The maximum number of stored permits. */
  double maxPermits;

  
The interval between two unit requests, at our stable rate. E.g., a stable rate of 5 permits
per second has a stable interval of 200ms.

/**
   * The interval between two unit requests, at our stable rate. E.g., a stable rate of 5 permits
   * per second has a stable interval of 200ms.
   */
  double stableIntervalMicros;

  
The time when the next request (no matter its size) will be granted. After granting a request,
this is pushed further in the future. Large requests push this further than small requests.

/**
   * The time when the next request (no matter its size) will be granted. After granting a request,
   * this is pushed further in the future. Large requests push this further than small requests.
   */
  private long nextFreeTicketMicros = 0L; // could be either in the past or future

  private SmoothRateLimiter(SleepingStopwatch stopwatch) {
    super(stopwatch);
  }

  @Override
  final void doSetRate(double permitsPerSecond, long nowMicros) {
    resync(nowMicros);
    double stableIntervalMicros = SECONDS.toMicros(1L) / permitsPerSecond;
    this.stableIntervalMicros = stableIntervalMicros;
    doSetRate(permitsPerSecond, stableIntervalMicros);
  }

  abstract void doSetRate(double permitsPerSecond, double stableIntervalMicros);

  @Override
  final double doGetRate() {
    return SECONDS.toMicros(1L) / stableIntervalMicros;
  }

  @Override
  final long queryEarliestAvailable(long nowMicros) {
    return nextFreeTicketMicros;
  }

  @Override
  final long reserveEarliestAvailable(int requiredPermits, long nowMicros) {
    resync(nowMicros);
    long returnValue = nextFreeTicketMicros;
    double storedPermitsToSpend = min(requiredPermits, this.storedPermits);
    double freshPermits = requiredPermits - storedPermitsToSpend;
    long waitMicros =
        storedPermitsToWaitTime(this.storedPermits, storedPermitsToSpend)
            + (long) (freshPermits * stableIntervalMicros);

    this.nextFreeTicketMicros = LongMath.saturatedAdd(nextFreeTicketMicros, waitMicros);
    this.storedPermits -= storedPermitsToSpend;
    return returnValue;
  }

  
Translates a specified portion of our currently stored permits which we want to spend/acquire,
into a throttling time. Conceptually, this evaluates the integral of the underlying function we
use, for the range of [(storedPermits - permitsToTake), storedPermits].

This always holds: 0 <= permitsToTake <= storedPermits 
/**
   * Translates a specified portion of our currently stored permits which we want to spend/acquire,
   * into a throttling time. Conceptually, this evaluates the integral of the underlying function we
   * use, for the range of [(storedPermits - permitsToTake), storedPermits].
   *
   * <p>This always holds: {@code 0 <= permitsToTake <= storedPermits}
   */
  abstract long storedPermitsToWaitTime(double storedPermits, double permitsToTake);

  
Returns the number of microseconds during cool down that we have to wait to get a new permit.

/**
   * Returns the number of microseconds during cool down that we have to wait to get a new permit.
   */
  abstract double coolDownIntervalMicros();

  
Updates storedPermits and nextFreeTicketMicros based on the current time. 
/** Updates {@code storedPermits} and {@code nextFreeTicketMicros} based on the current time. */
  void resync(long nowMicros) {
    // if nextFreeTicket is in the past, resync to now
    if (nowMicros > nextFreeTicketMicros) {
      double newPermits = (nowMicros - nextFreeTicketMicros) / coolDownIntervalMicros();
      storedPermits = min(maxPermits, storedPermits + newPermits);
      nextFreeTicketMicros = nowMicros;
    }
  }
}